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Overview
This monograph presents interactive mathematics within a self-contained framework, the cone separation technique. This framework affords a unified approach to multiple objective decision problems and their most common model, the vector optimization problem, regardless of their linear, discrete, continuous, convex, or nonconvex nature. With this approach, the analysis of relations between efficient decisions is significantly broadened, new facts are identified and proved.
The cone separation technique gives the decision maker or researcher better methods for analyzing potential efficiency solutions. Specifically, the framework can add any of the following to a solution: a simple way of creating hierarchical structures over sets of efficient decisions; a way of visualizing the decision making process by a method of graphic approximation; a method to calculate trade-offs and gain-to-loss ratios; and sensitivity analysis of efficient solutions with respect to perturbation analysis. It is the first monograph which interprets elements of interactive, multiple-objective decision making in terms of cone separation. The book treats the topic formally, but the mathematics is subordinate to the technique of seeking results to assist decision making.
Synopsis
This monograph presents interactive mathematics within a self-contained framework, the cone separation technique. This framework affords a unified approach to multiple objective decision problems and their most common model, the vector optimization problem, regardless of their linear, discrete, continuous, convex, or nonconvex nature. With this approach, the analysis of relations between efficient decisions is significantly broadened, new facts are identified and proved.
The cone separation technique gives the decision maker or researcher better methods for analyzing potential efficiency solutions. Specifically, the framework can add any of the following to a solution:
- a simple way of creating hierarchical structures over sets of efficient decisions;
- a way of visualizing the decision making process by a method of graphic approximation;
- a method to calculate trade-offs and gain-to-loss ratios; and
- sensitivity analysis of efficient solutions with respect to perturbation analysis.
Booknews
Explains a framework for addressing multiple objective decision problems regardless of whether they are linear, discrete, continuous, convex, or non-convex. Interactive mathematics within the framework can be used to create hierarchical structures over sets of efficient decisions, visualize the decision making process with graphic approximations, calculate trade-offs, and perform other tasks. Assumes knowledge of vector optimization and multiple objective decision making. Annotation c. Book News, Inc., Portland, OR (booknews.com)